Overview

I am undertaking a PhD in Theoretical Physics under the supervision of Dr. Simon Horsley and Prof. Geoff Nash, as part of the EPSRC Centre for Doctoral Training in Metamaterials. 

My PhD focuses on controlling reflection by designing graded-index structures. At the heart of any wave phenomena is a Helmholtz-type equation. This means that we can draw parallels between electromagnetic, acoustic, or even quantum mechanical waves. We take advantage of this wave-equivalence to adopt and combine mathematical frameworks and wave phenomena in quantum mechanics in order to design bespoke optical media that have specific reflection properties. In particular, we use so-called half-bound states that arise in quantum mechanics in order to design graded-index dielectrics that will not reflect waves, for a fixed polarisation, at grazing incidence - a delicate limit that usually results in complete reflection. This could be useful, for example, to minimise radar cross sections.

Moving onto thermal bodies, we use the fluctuation-dissipation theorem in order to mathematically characterise the properties of a thermal emitter consisting of multi-layer grapene. The inclusion of an aluminium back reflector on the device does not obey the standard Planck spectrum. By formulating a theory of non thermal equilibrium radiation, our mathematical framework allows us to model experimental data, and extract estimates for the operating temperature of the graphene multi-layer. We extend this to show that under certain approximations, our results reduce down to the well understoon Kirchoff's law of thermal radiation.

Finally we extend our search to manipulate the spectral response of materials by looking into the complex frequency domain. Here we find poles in reflection, which are attributed to quasi-normal modes. These modes can be used to reconstruct the spectral response of a material by relating the real and imaginary component of the complex frequency of the mode to the resonant frequency and linewidth respectively to the resonant response. By formulating an `eigen-permittivity' approach, we can determine a global permittivity index shift that would be required in order to ensure that a quasi-normal mode exists at a pre-determined complex frequency.

View my thesis here: https://ore.exeter.ac.uk/repository/handle/10871/132694

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